Of a single sinusoidal component, sure, this is true. But phase differences between sonic features are absolutely detectable.

The effect is most noticeable on raw synthesized tones: sawtooth, square wave, etc. These tones contain sonic energy concentrated at discontinuities in the waveforms. The ear can hear this, as a "buzzing sound".

Run these tones through Paulstretch (even with 0 stretch), and the sonic energy is distributed throughout the wavecycle. These tones retain their spectral character, but noticeably lose the buzzing character.

I've uploaded a demo here: https://chris.pacejo.net/temp/phase.wav It is a 55 Hz sawtooth tone, alternating every 2.5 s between the raw tone, and the tone fed through Paulstretch with no stretching.

There was even a paper written on this. Laitinen, Disch & Pulkki, "Sensitivity of Human Hearing to Changes in Phase Spectrum". [1]

Paulstretch muddies up percussive transients (like hi hat strikes) as well.

Anyway it's the reason things like gammatone filters exist for analyzing audio. They reveal phase correlations in the same way the ear is able to. Windowed Fourier transforms (used by e.g. Paulstretch and Audacity for various purposes) obfuscate these relationships.

Aside: please try to avoid snarky armchair dismissals on HN: https://news.ycombinator.com/newsguidelines.html "you are trying to sound intelligent" does not advance discourse.

[1] https://www.researchgate.net/profile/Ville-Pulkki/publicatio...

A 6-Hour Time-Stretched Version of Brian Eno's Music for Airports